An Illustration of the Effects of Fluctuations in Test Information on Measurement Error, the Attenuation of Effect Sizes, and Diagnostic Reliability
Measurement precision often fluctuates across latent trait continuums. Plots of test information are typically provided in item response theory (IRT) investigations, but the numerical values for test information are not readily interpretable. This article draws attention to the important, nonlinear relationships between test information, location-specific standard errors of measurement, and location-specific reliability. It provides a method for examining the attenuation in effect sizes (correlations) that is caused by fluctuating levels of measurement error. It also outlines the conditions under which fluctuating measurement error influences effect sizes. The effect of fluctuating error on effect sizes can be more serious than what is predicted by the well-known correction for attenuation formula that is based on constant reliability coefficients. The relationship between levels of test information and diagnostic reliability is also examined. Higher levels of test information are required for diagnostic reliability than for the prevention of effect size attenutation. Data from previously published IRT studies in personality and abnormal psychology are used to illustrate these phenomena.